Simplify the following expression: $n = \dfrac{30r + 5}{-10r}$ You can assume $r \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $30r + 5 = (2\cdot3\cdot5 \cdot r) + (5)$ The denominator can be factored: $-10r = - (2\cdot5 \cdot r)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $n = \dfrac{(5)(6r + 1)}{(5)(-2r)}$ Dividing both the numerator and denominator by $5$ gives: $n = \dfrac{6r + 1}{-2r}$